THE ASYMPTOTIC BEHAVIOR AND SYMMETRY OF POSITIVE SOLUTIONS TO p-LAPLACIAN EQUATIONS IN A HALF-SPACE

被引：1

作者：

Chen, Yujuan ^{[1
]}

Wei, Lei ^{[2
]}

Zhang, Yimin ^{[3
]}

机构：

[1] Nantong Univ, Sch Sci, Nantong 226007, Peoples R China

[2] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

[3] Wuhan Univ Technol, Ctr Math Sci, Wuhan 430070, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2022年 / 42卷 / 05期

关键词：

p-Lapacian; Hardy potential; symmetry; uniqueness; asymptotic behavior; SEMILINEAR ELLIPTIC-EQUATIONS; BLOW-UP SOLUTIONS; MAXIMUM;

D O I：

10.1007/s10473-022-0524-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a nonlinear equation in the half-space with a Hardy potential, specifically, -Delta(p)u = lambda u(p-1)/x(1)(p) - x(1)(theta) f(u) in T, where Delta(p) stands for the p-Laplacian operator defined by Delta(p)u = div(vertical bar del u vertical bar(p-2)del u), p > 1, theta > -p, and T is a half-space {x(1) > 0}. When lambda > Theta (where Theta is the Hardy constant), we show that under suitable conditions on f and theta, the equation has a unique positive solution. Moreover, the exact behavior of the unique positive solution as x(1) -> 0(+), and the symmetric property of the positive solution are obtained.

引用

页码：2149 / 2164

页数：16

共 50 条

[1] The Asymptotic Behavior and Symmetry of Positive Solutions to p-Laplacian Equations in a Half-Space
Yujuan Chen
Lei Wei
Yimin Zhang
Acta Mathematica Scientia, 2022, 42 : 2149 - 2164
[2] THE ASYMPTOTIC BEHAVIOR AND SYMMETRY OF POSITIVE SOLUTIONS TO p-LAPLACIAN EQUATIONS IN A HALF-SPACE
陈玉娟
魏雷
张贻民
ActaMathematicaScientia, 2022, 42 (05) : 2149 - 2164
[3] Asymptotic behaviour and symmetry of positive solutions to nonlinear elliptic equations in a half-space
Wei, Lei
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2016, 146 (06) : 1243 - 1263
[4] SYMMETRY AND NONEXISTENCE OF POSITIVE SOLUTIONS TO FRACTIONAL P-LAPLACIAN EQUATIONS
Wu, Leyun
Niu, Pengcheng
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2019, 39 (03) : 1573 - 1583
[5] Symmetry of positive solutions for Choquard equations with fractional p-Laplacian
Ma, Lingwei
Zhang, Zhenqiu
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 182 : 248 - 262
[6] ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS FOR THE RADIAL P-LAPLACIAN EQUATION
Ben Othman, Sonia
Maagli, Habib
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2012,
[7] Asymptotic Behavior of Positive Solutions of a Nonlinear Combined p-Laplacian Equation
Maagli, Habib
Chemmam, Rym
Ben Othman, Sonia
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2014, 11 (03) : 857 - 872
[8] EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO NONLINEAR RADIAL p-LAPLACIAN EQUATIONS
Masmoudi, Syrine
Zermani, Samia
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
[9] Asymptotic Behavior of Positive Solutions of a Nonlinear Combined p-Laplacian Equation
Habib Mâagli
Rym Chemmam
Sonia Ben Othman
Mediterranean Journal of Mathematics, 2014, 11 : 857 - 872
[10] Asymptotic behavior of the solutions of the p-Laplacian equation
Zhang Liqin
Zhao Junning
SCIENCE IN CHINA SERIES A-MATHEMATICS, 2006, 49 (06): : 740 - 751

← 1 2 3 4 5 →